This paper reports a detailed study of a graphene-based metasurface to function as tunable broadband linear to circular polarization converter in the terahertz gap. This device provides a wide polarization conversion band of 2.25 THz (3.75 THz to 6 THz) with an enhanced fractional 3-dB axial ratio bandwidth (FARBW) of 46.15%. The proposed structure consists of a simple tri-layer configuration where the meta-atom comprises a patterned graphene layer on a gold-backed silicon dioxide substrate. The proposed reflective-type linear to circular polarization converter (RLCPC) exhibits both right-handed and left-handed circular orientations of the reflected wave in two halves of the operating spectrum, further validated in terms of polarization ellipses developed by an inhouse code. The lack of experimental setup at the above said frequencies available to the authors in their country has been paid off by verifying the response using a detailed circuit model. The RLCPC maintains a thickness of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ<sub>o</sub></i> /7.69 with a lattice size of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ<sub>o</sub></i> /8.33. The structure also promises a stable wideband circular polarization conversion up to 20° and a dual-band circular polarization conversion up to 40° incident angle of the electromagnetic wave. This device can be useful for THz beam scanning antennas, RCS reduction and THz antennas for space and military radar applications.